Physics
An egg sinks in soft water but floats in a concentrated solution of salt because

Albumin dissolves in salt solution and egg becomes lighter
Water has high surface tension
Egg absorbs salt from the solution and expands
The density of salt solution exceeds the density of eggs

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Physics
A drop of liquid assumes spherical shape because:

A sphere has the least surface area for a given volume
Inter molecular forces are weak in liquids
A sphere has the largest surface area for a given volume
Intermolecular forces are strong in liquids

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